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This Perspective paper deals with an overview of particle-in-cell/Monte Carlo collision models applied to different plasma-propulsion configurations and scenarios, from electrostatic (E × B and pulsed arc) devices to electromagnetic (RF inductive, helicon, electron cyclotron resonance) thrusters, as well as plasma plumes and their interaction with the satellite. The most important items related to the modeling of plasma–wall interaction are also presented. Finally, the paper reports new progress in the particle-in-cell computational methodology, in particular, regarding accelerating computational techniques for multi-dimensional simulations and plasma chemistry Monte Carlo modules for molecular and alternative propellants. [ABSTRACT FROM AUTHOR]

In Paper I [Garrigues et al., Phys. Plasmas 31, 073907 (2024)], we have extended the sparse PIC approach already used in the literature with the offset scheme to reduce the grid-based error. In this study, we demonstrate the ability of the offset sparse PIC algorithm to model partially magnetized low-temperature plasmas by reducing the grid-based error. In the context of multi-cusp magnetic field configurations, the offset scheme reduces the error of the current collected at the walls to less than 5 % for more of the plasma conditions encountered in ion source applications. The formation of a double layer in the sheath region is also captured. In the context of the electron drift instability that occurs in the Hall thruster, the plasma properties as well as the ion velocity distribution function can be retrieved with a high enough precision without considering an initial regular grid with a smaller mesh resolution. The results also highlight the advantage of combining the electric potential at the nodes of the regular grid instead of directly combining the electric field from the component grids. Compared to the regular PIC algorithm, the typical speed-up factor is about three for a number of mesh nodes of 256 2 and five for 512 2 . [ABSTRACT FROM AUTHOR]

The use of sparse particle-in-cell (PIC) algorithms to accelerate the standard explicit PIC scheme has recently been successfully applied in the context of single-frequency capacitively coupled plasma discharges [Garrigues et al., J. Appl. Phys. 129, 153303 (2021)]. We have extended the sparse PIC scheme to model dual-frequency capacitive discharges. Comparisons between standard and sparse PIC algorithms show that the plasma properties as well as the electron and ion distribution functions can be retrieved with a maximum error of 2%. This work opens the interest of using the sparse PIC algorithm to perform 2D and 3D simulations under real operating conditions of capacitively coupled plasma discharges. [ABSTRACT FROM AUTHOR]

Hall thrusters are E × B plasma devices characterised by a large azimuthal electron current, which is involved in the formation of a wide variety of instabilities on different frequency scales (from kilohertz to gigahertz) and propagating in different directions. We have focused on a limited number of low-frequency instabilities that could be experimentally observed, such as breathing mode (BM) and ion transit time oscillations (ITTO). There are still gray areas in the understanding of the mechanisms behind these instabilities, which are often described individually, without considering an eventual exchange of information between the different types of instability. A wavelet time-frequency study of the plasma revealed the coexistence and interdependence of distinct instabilities. We suspect a possible interaction between the breathing mode and higher-frequency oscillations leading to ITTOs: it was shown that a transition occurred when the frequency of one of the BM harmonics became a multiple of the frequency of the higher-frequency oscillations. This was also accompanied by a deformation of the ion energy distribution functions. [ABSTRACT FROM AUTHOR]

In this Tutorial, we consider plasma sources with applications to fusion devices and high energy accelerators. These ion sources typically produce negative ions from hydrogen-isotope gases, which are extracted through one or multiple apertures and accelerated to high kinetic energies. Next, they are either double stripped of two electrons to form positive ions used as precursors in accelerator devices or neutralized to produce a neutral beam injected in tokamak reactors. Contrary to the working conditions of most ion sources where volume production prevails, the mechanism of negative ion production by dissociative electron attachment on vibrationally excited molecules inside the plasma volume of fusion-type hydrogen-fueled high power discharges is mostly balanced by their destruction by detachment before being extracted rendering this means of producing negative ions rather inefficient. Surface production through the transfer of electrons from low work function metallic materials to the impacting atoms is the alternative solution to fulfill the requirements for the applications concerned. Negative ions are produced close to the aperture from which they are extracted. As a result, the analysis and understanding of the extraction mechanisms through experimental diagnostics is rather difficult due to the lack of accessibility and can only give a partial view. In addition, most of the experimental work is focused on the validation of requirements for the applications and not to the investigation of the fundamental processes that take place inside these types of sources. This Tutorial is focused on the description and understanding of the physical mechanisms behind the extraction and acceleration of negative ions from hydrogen plasma sources through modeling methods. We describe the numerical techniques of particle-based methods with a specific emphasis on particle-in-cell Monte Carlo collision algorithms. An analysis of the physical processes involved in driving the negative ions from the plasma source, across the apertures and inside the accelerator as reported in the literature, is presented in detail. This Tutorial concludes with additional and future works to be addressed in the coming years. [ABSTRACT FROM AUTHOR]

More and more CubeSats are being launched. On these small platforms, subsystems such as propulsion and communication ones have to coexist. This article focuses on electromagnetic interaction between these two critical subsystems. Hence, a numerical multi-physics method is proposed in order to quantify perturbation caused by an electric thruster's plume on the antenna of a CubeSat type spacecraft. A plume simulation model has been coupled with electromagnetic simulation software. As an example, the farfield radiation patterns and radioelectric characteristics of a 436 MHz dipole are presented when located near a Hall thruster's plume on a 6U type platform. Changes in radiation patterns are observed in the presence of plume for the dipole antenna. This versatile method makes it possible to represent microwave propagation through a plume for various antennas, thruster's plumes, or relative positions. [ABSTRACT FROM AUTHOR]

Three-dimensional simulations of partially magnetized plasma are real challenges that actually limit the understanding of the discharge operations such as the role of kinetic instabilities using explicit Particle-In-Cell (PIC) schemes. The transition to high performance computing cannot overcome all the limits inherent to very high plasma densities and thin mesh sizes employed to avoid numerical heating. We have applied a recent method proposed in the literature [L. F. Ricketson and A. J. Cerfon, Plasma Phys. Controlled Fusion 59, 024002 (2017)] to model low temperature plasmas. This new approach, namely, the sparse grid combination technique, offers a gain in computational time by solving the problem on a reduced number of grid cells, hence allowing also the reduction of the total number of macroparticles in the system. We have modeled the example of the two-dimensional electron drift instability, which was extensively studied in the literature to explain the anomalous electron transport in a Hall thruster. Comparisons between standard and sparse grid PIC methods show an encouraging gain in the computational time with an acceptable level of error. This method offers a unique opportunity for future three-dimensional simulations of instabilities in partially magnetized low temperature plasmas. [ABSTRACT FROM AUTHOR]

The use of a particle-in-cell (PIC) algorithm with an explicit scheme to model low temperature plasmas is challenging due to computational time constrains related to resolving both the electron Debye length in space and the inverse of a fraction of the plasma frequency in time. One recent publication [Ricketson and Cerfon, Plasma Phys. Control. Fusion 59, 024002 (2017)] has demonstrated the interest of using a sparse grid combination technique to accelerate the explicit PIC model. Simplest plasma conditions were considered. This paper is the demonstration of the capability and the effectiveness of the sparse grid combination technique embedded in the PIC algorithm (hereafter called "sparse PIC") to self-consistently model capacitively coupled radio frequency discharges. For two-dimensional calculations, the sparse PIC approach is shown to accurately reproduce the plasma profiles and the energy distribution functions compared to the standard PIC model. The plasma parameters obtained by these two numerical methods differ by less than 5%, while a speed up in the executable time between 2 and 5 is obtained depending on the setup. [ABSTRACT FROM AUTHOR]

The effects of electron-wall interactions on cross magnetic field electron momentum and energy losses in Hall effect thrusters are studied. The results suggest that the electron-wall interactions do not play a very important role in the electron momentum balance in the channel, as the anomalous conductivity is only due to the microturbulence or field fluctuations.

The Particle-In-Cell Monte Carlo Collision (PIC MCC) method has been used by different authors in the last ten years to describe negative ion extraction in the context of neutral beam injection for fusion. Questionable results on the intensity and profile of the extracted negative ion beamlets have been presented in several recently published papers. Using a standard explicit PIC MCC method, we show that these results are due to a non-compliance with the constraints of the numerical method (grid spacing, number of particles per cell) and to a non-physical generation of the simulated plasma. We discuss in detail the conditions of mesh convergence and plasma generation and show that the results can significantly deviate from the correct solution and lead to unphysical features when the constraints inherent to the method are not strictly fulfilled. This paper illustrates the importance of verification in any plasma simulation. Since the results presented in this paper have been obtained with careful verification of the method, we propose them as benchmarks for future comparisons between different simulation codes for negative ion extraction. [ABSTRACT FROM AUTHOR]

Research was conducted to determine the electrical properties of stationary plasma thrusters and the low frequency oscillation regime. The model was based on the assumption of quasineutrality of the plasma column and on a 1D transient hybrid treatment of electron and ion transport in the device. The model offers reasonable calculations of the plasma properties and can give a clear picture of the low frequency oscillations.

Operation of a 5 kW-class Hall current Thruster for various voltages from 400V to 800V and a xenon mass flow rate of 6mg s-1 have been studied with a quasi-neutral hybrid model. In this model, anomalous electron transport is fitted from ion mean velocity measurements, and energy losses due to electron-wall interactions are used as a tuned parameter to match expected electron temperature strength for same class of thruster. Doubly charged ions production has been taken into account and detailed collisions between heavy species included. As the electron temperature increases, the main channel of Xe2+ ion production becomes stepwise ionization of Xe+ ions. For an applied voltage of 800 V, the mass utilization efficiency is in the range of 0.8-1.1, and the current fraction of doubly charged ions varies between 0.1 and 0.2. Results show that the region of ion production of each species is located at the same place inside the thruster channel. Because collision processes mean free path is larger than the acceleration region, each type of ions experiences same potential drop, and ion energy distributions of singly and doubly charged are very similar. [ABSTRACT FROM AUTHOR]

In this paper we propose a representative simulation test-case of E × B discharges accounting for plasma wall interactions with the presence of both the electron cyclotron drift instability and the modified-two-stream-instability. Seven independently developed particle-in-cell (PIC) codes have simulated this benchmark case, with the same specified conditions. The characteristics of the different codes and computing times are given. Results show that both instabilities were captured in a similar fashion and good agreement between the different PIC codes is reported as main plasma parameters were closely related within a 5% interval. The number of macroparticles per cell was also varied and statistical convergence was reached. Detailed outputs are given in the supplementary data, to be used by other similar groups in the perspective of code verification. [ABSTRACT FROM AUTHOR]

An end-Hall ion source is a cylindrical magnetized device of few centimeters in length able to generate an ion beam with a current of typically 1 A and ion energies in the range of 100 eV. This ion source does not use acceleration grids, has a relatively large ion beam divergence, and is well suited for ion assisted deposition processes. In this paper, a self-consistent two-dimensional quasi-neutral model of an end-Hall ion source is used to understand the parameters controlling the characteristics of the extracted. The model results underline the role of charge exchange collisions on beam properties. The calculated energy distribution functions reveal the existence of groups of slow ions and fast neutrals. Ion mean energy corresponds to roughly 60% of the discharge voltage, while the root mean square deviation from the mean energy corresponds to about 33% of the discharge voltage, as in experiments. The influence of the position of the electron emitting source on the ion angular distribution is also shown. [ABSTRACT FROM AUTHOR]

We compare time-averaged and time-varying measured and computed ion velocity distribution functions in a Hall effect thruster for typical operating conditions. The ion properties are measured by means of laser induced fluorescence spectroscopy. Simulations of the plasma properties are performed with a two-dimensional hybrid model. In the electron fluid description of the hybrid model, the anomalous transport responsible for the electron diffusion across the magnetic field barrier is deduced from the experimental profile of the time-averaged electric field. The use of a steady state anomalous mobility profile allows the hybrid model to capture some properties like the time-averaged ion mean velocity. Yet, the model fails at reproducing the time evolution of the ion velocity. This fact reveals a complex underlying physics that necessitates to account for the electron dynamics over a short time-scale. This study also shows the necessity for electron temperature measurements. Moreover, the strength of the self-magnetic field due to the rotating Hall current is found negligible. [ABSTRACT FROM AUTHOR]

During the postarc dielectric recovery phase in a vacuum circuit breaker, a cathode sheath forms and expels the plasma from the electrode gap. The success or failure of current breaking depends on how efficiently the plasma is expelled from the electrode gap. The sheath expansion in the postarc phase can be compared to sheath expansion in plasma immersion ion implantation except that collisions between charged particles and atoms generated by electrode evaporation may become important in a vacuum circuit breaker. In this paper, we show that electrode evaporation plays a significant role in the dynamics of the sheath expansion in this context not only because charged particle transport is no longer collisionless but also because the neutral flow due to evaporation and temperature gradients may push the plasma toward one of the electrodes. Using a hybrid model of the nonequilibrium postarc plasma and cathode sheath coupled with a direct simulation Monte Carlo method to describe collisions between heavy species, we present a parametric study of the sheath and plasma dynamics and of the time needed for the sheath to expel the plasma from the gap for different values of plasma density and electrode temperatures at the beginning of the postarc phase. This work constitutes a preliminary step toward understanding and quantifying the risk of current breaking failure of a vacuum arc. [ABSTRACT FROM AUTHOR]

Stationary plasma thrusters (SPTs) are advanced propulsion devices that use a gas discharge to ionize and accelerate the propellant. We present simulation results obtained with a two-dimensional hybrid model of an SPT discharge. The model characterizes the ill-understood anomalous electron transport in SPTs by empirical parameters, of which we demonstrate the influence on the simulation results. Although no optimal values for these parameters can clearly be identified, the model predicts many features of the SPT behavior and yields interesting insights in the SPT physics. Experimentally observed electric potential distributions can only be reproduced if the anomalous electron transport is assumed to be stronger outside than inside the SPT channel. The simulations reproduce experimentally measured oscillations at 10-20 kHz and predict additional oscillations at 100-200 kHz. We discuss the dynamics of these oscillations and their influence on the energy distribution of the ion beam leaving the thruster. [ABSTRACT FROM AUTHOR]

We have developed a two-dimensional hybrid fluid — particle-in-cell Monte Carlo collisions (PIC-MCC) model to study the plume of a stationary plasma thruster. The model is based on a fluid description of the electrons (the electron density follows a Boltzmann distribution) and a particle description of the ion and neutral transport. Collisions between heavy species are taken into account with a Monte Carlo method. The electric field is obtained from Poisson's equation or from the quasineutrality assumption. We first show that the results from the PIC-MCC model are close to the results of a more time-consuming direct simulation Monte Carlo approach. We then compare the model predictions of the plume density and ion energy distribution with experimental measurements. Finally, we present a brief discussion on the assumptions of the model and on its ability to give reliable predictions on important issues such as the flux of ions backscattered to the satellite. [ABSTRACT FROM AUTHOR]

Stationary plasma thrusters (SPTs) are advanced propulsion devices that use a gas discharge to ionize and accelerate the propellant. We present in detail a two-dimensional model of an SPT discharge. The model combines a particle simulation of neutral atoms and ions with a fluid description of electrons, where the electric field is obtained from imposing quasineutrality. The electron mobility and energy loss are treated in an empirical way and characterized by ad hoc parameters. Typical simulation results are shown. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Hall effect thrusters (HETs) are ion sources used for satellite station keeping and orbit raising. In Single Stage HETs, the same electric field is responsible for electron heating and ion acceleration. We present a new HET concept where ionization and acceleration are separated in two different stages. This double stage HET allows for a more versatile operation and a separate control of thrust and specific impulse. Index Terms--Electric propulsion, Hall effect thruster (HET), hybrid model, ion source.